The simulation devices and methods are known in the prior art and widely used, and take advantage of the ever increasing power of computers. FIG. 1 is an illustration of a case of complex simulation. In that example, an operator (100) manipulates a stylus (110), which is connected to an articulated mechanical assembly (115) capable of producing forces that oppose the movement of said stylus. The operator moves the stylus by viewing its movement on an image displayed by a screen (120). The image represents a deformable solid (130) of any shape, which can be defined by its shape, dimensions, and the material or materials of which it is made. The articulated device (115) and the display of the image on the screen (120) are managed by a computer (150) that computes a model representing a solid (130) and providing the response of that solid, in the form of components of a force that reacts to a movement imposed at a given point. Because the properties of the solid (130) are known, it is possible to compute its response to a movement of the stylus, measured by the articulated system (115) and in return, to control the actuators of said articulated system (115) so that they apply against that movement a force with a given intensity and spatial direction, in proportion with the computed response of the solid (130). The result of the computation also makes it possible to view the computed deformation of the solid on the screen (120). Such a device is known as a haptic interface. According to the prior art, the mechanical response of the solid (130) to the application of a movement or a force with a given intensity and direction at any point of its surface can be computed by techniques using finite elements. The time for resolving each case of loading depends on the computing power that can be mobilized by the computer (150). For such an application, which is within the scope of augmented virtual reality, if the operator is to experience sensations comparable to actual interaction with the solid, the display must be updated at least 24 times every second, and regarding the resistance force, in order to reproduce the feeling of touch, the control of the actuators of the articulated mechanical assembly (115) must be updated several hundred times every second. Even in a simple case like this one, the computation speed required is to date out of the reach of computers or would require the use of computing means out of proportion with the sought objective. The problem of the computing power is even more acute when said computing means (150) must be of the on-board type, for instance on board a vehicle. Thus, one solution of the prior art for such a problem consists in computing beforehand or in offline mode a discrete solution with a sufficient density of points, which solution is then saved in the form of tables that are merely read back during real-time simulation. However, while such a solution makes it possible to achieve the required execution speeds with limited computing power, it is limited by the quantity of information to save. Thus, in this exemplary embodiment, if the surface of the solid (130) is discretized into Ns points, firstly, one needs to compute the intensity of the force (F) defined by a vector F and its three spatial components Fx, Fy and Fz, opposing an imposed movement (D), also defined by a vector D (140) and its spatial components Dx, Dy and Dz, regardless of the point of application (131) of the imposed movement from the Ns points, for the haptic interface.
Besides, for the visual interface, the movement of each of the Ns points of the solid must be computed; such movement is defined for each of the Ns points by a vector U and its three spatial components Ux, Uy and Uz, which vector must be defined regardless of the point of application (131) of the imposed movement (140) and regardless of the movement D imposed at that point.
In the prior art, the studied range of variation of the imposed movement is discretized into nd possibilities, where each component Dx, Dy and Dz can have nd values out of the Nd possibilities, so that Nd=nd.nd.nd=nd3.
Thus, according to the prior art, computation is carried out by a computation code using for example the finite-element method, for all the possible combinations, and the corresponding results are stored in a table. Thus, to obtain the table, Nd×Ns simulations must be carried out. In one exemplary embodiment, if Nd=106, or 100 discretizing points per component, and Ns=100, then 108 simulations will be necessary. At the rate of 0.1 seconds per simulation, which can only be reached if the computation power is particularly high, nearly 12 days will be needed to carry out the computations required and close to a year if each simulation takes three seconds.
Then, to store all the solutions in a table, 3×Nd×Ns×Ns results will have to be stored regarding the movement U of each of the Ns points of the surface of the solid to cover each case of loading, and 3×Nd×Ns results for the components of the force and for all cases of loading. Thus, if Nd=106 and Ns=100, the quantity of information to save is 3·(1010+108), or 30.3 gigabytes if each result is coded in 8 bits. Further, if finer resolution is required for the movement, so as to allow more frequent updating of the haptic interface, the quantity of data to save increases exponentially and the limits for storage are soon reached, particularly in on-board systems.
Hereinafter, “real-time” relates to a computation time below 0.04 seconds between two states of the simulated system or process, and “complex” applies to systems or processes where the simulated operating range can cover at least 106 distinct states.
Another solution of the prior art consists in using an extremely simplified representation that only creates an illusion of actual behavior. Such solutions are commonly used in video games, but are too far removed from reality for use that requires a certain standard of safety such as the driving of vehicles or processes.
The examples of application above and the field of application of the method according to the invention are within the field of methods and devices known as DDDAS, standing for Dynamic Data Driven Applications Systems, which allow the real-time control of a simulation, for example through data from sensors, and in return, the ability to drive the system or process generating the data from updated simulation results. Such applications are currently limited by the “curse of dimensionality” as described above.